Bimetallic Strip Bending Angle

1. Jan 27, 2009

tejas710

Hi! There is a thermodynamics problem which I seem to be able to understand, yet unable to solve. If someone can me with it I would appreciate it.
1. The problem statement, all variables and given/known data
A Bi-metallic strip is straight at T= T0. It curves as it is heated up due to unequal expansion of two metals. The strip is made up of iron (a = 1.2e-5) and zinc (a = 3.1e-5). The question asks to calculate the bending angle when the original length of the strip is 100mm and with thickness of 1 mm.

2. Relevant equations
The linear expansion equation: L = L0(1 + a(T2 - T0))

3. The attempt at a solution
The substituted equations: LI = (100)(1 + (1.2e-5)($$\Delta$$T)
LZ = (100)(1 + (3.1e-5)($$\Delta$$T)

From here I use the formula s = r$$\theta$$
and get $$\theta$$ = (3.8e-3)($$\Delta$$T)

I am not sure how to proceed from here because the question asks for a numerical answer but that seems impossible without the temperatures given.

2. Jan 27, 2009

LowlyPion

Welcome to PF.

If they give no temperature rise, then leave your answer in terms of ΔT as you have.

3. Jan 27, 2009

tejas710

Thanks. I guess I will leave it as an expression.

4. Feb 1, 2009

Poptor, eh?

5. Feb 1, 2009

faiyth

Sorry for the double-post, but also.. I don't understand your solution.

What does s=r*Theta have to do with this question.. and how does that lead to your solution?

6. Feb 1, 2009

LowlyPion

The displacement of the end is given by the angle times the radius for small angle displacements.

7. Feb 1, 2009

faiyth

Oh.. what exactly is the radius in this question?
I guess it's just that he said:

3. The attempt at a solution
The substituted equations: LI = (100)(1 + (1.2e-5)(LaTeX Code: \\Delta T)
LZ = (100)(1 + (3.1e-5)(LaTeX Code: \\Delta T)

From here I use the formula s = rLaTeX Code: \\theta
and get LaTeX Code: \\theta = (3.8e-3)(LaTeX Code: \\Delta T)

I sense a really big logic gap missing..

Otherwise, I thought the appropriate formula was:

Theta = length / thickness * (a1 - a2)*(T2-T1)

Where a1 and a2 are the expansion coefficients, and T2 and T1 are temperatures.

Excuse my ignorance, and thanks for the help.